18
Valuation and Capital
Budgeting for the Levered Firm
In September 2014, Tesla announced that it would build a
$5 billion “gigafactory” in Nevada. So why did Tesla choose
Nevada? A major reason was a package granted to the company consisting of $1.25 billion in tax breaks and other perks.
For example, Tesla received a 20-year sales tax abatement
worth $725 million, a 10-year property tax abatement worth
$332 million, and discounted electricity rates for eight years,
worth $8 million. The package was the largest ever offered
by Nevada and one of the largest ever in the United States.
When a corporation opens a major plant or considers
relocation, municipalities often create packages loaded with
subsidies such as these. Other common subsidies include
subsidized debt, educational training, and road and infrastructure creation.
With subsidized debt, a state or municipality guarantees
the debt, which allows the company to borrow at a much
lower interest rate. If the interest rate on the debt is lower
than the company’s normal cost of debt, how does the firm
evaluate the financial benefits of this and other such subsidies?
In this chapter, we illustrate how to evaluate projects using
the adjusted present value and flows to equity approaches to
valuation to answer this and related questions.
18.1 Adjusted Present Value Approach
In this chapter, we describe three approaches to valuation for the levered firm. In particular,
we describe the adjusted present value (APV) approach, the flow to equity (FTE) approach,
and the weighted average cost of capital (WACC) approach. As you may recognize, we have
discussed each of these approaches in previous chapters. The analysis of these approaches
is relevant for entire firms as well as projects. The specific purpose of this chapter is to tie
things together and show that each of the approaches is logically consistent with each other
and can give the same answer. However, at times, one approach might be easier to implement
than another, and we suggest guidelines for selecting between the approaches. We start with
the adjusted present value method.
The adjusted present value (APV) method is best described by the following formula:
APV 5 NPV 1 NPVF
In words, the value of a project to a levered firm (APV) is equal to the value of the project
to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF).
We can generally think of four side effects:
1. The tax subsidy to debt: This was discussed in Chapter 16, where we pointed out
that for perpetual debt the value of the tax subsidy is tC B. (tC is the corporate tax
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rate, and B is the value of the debt.) The material about valuation under corporate
taxes in Chapter 16 is actually an application of the APV approach.
2. The costs of issuing new securities: As we will discuss in detail in Chapter 20, investment bankers participate in the public issuance of corporate debt. These bankers must
be compensated for their time and effort, a cost that lowers the value of the project.
3. The costs of financial distress: The possibility of financial distress, and bankruptcy
in particular, arises with debt financing. As stated in the previous chapter, financial
distress imposes costs, thereby lowering value.
4. Subsidies to debt financing: The interest on debt issued by state and local governments is not taxable to the investor. Because of this, the yield on tax-exempt debt is
generally substantially below the yield on taxable debt. Frequently corporations can
obtain financing from a municipality at the tax-exempt rate because the municipality
can borrow at that rate as well. As with any subsidy, this subsidy adds value.
Although each of the preceding four side effects is important, the tax deduction to debt
almost certainly has the highest dollar value in most actual situations. For this reason, the following example considers the tax subsidy but not the other three side effects.1
Consider a project of the P. B. Singer Co. with the following characteristics:
Cash inflows: $500,000 per year for the indefinite future.
Cash costs: 72% of sales.
Initial investment: $475,000.
tC 5 34%
R0 5 20%, where R0 is the cost of capital for a project of an all-equity firm.
If both the project and the firm are financed with only equity, the project’s cash flow is as
follows:
Cash inflows
Cash costs
Operating income
$500,000
−360,000
Corporate tax (34% tax rate)
140,000
−47,600
Unlevered cash flow (UCF)
$ 92,400
The distinction between present value and net present value is important for this
example. The present value of a project is determined before the initial investment at Date
0 is subtracted. The initial investment is subtracted for the calculation of net present value.
Given a discount rate of 20 percent, the present value of the project is:
$92,400
_______
= $462,000
.20
The net present value (NPV) of the project—that is, the value of the project to an all-equity
firm—is:
$462,000 2 $475,000 5 2$13,000
Because the NPV is negative, the project would be rejected by an all-equity firm.
Now imagine that the firm finances the project with exactly $126,229.50 in debt, so
that the remaining investment of $348,770.50 (5 $475,000 2 $126,229.50) is financed
1
The Bicksler Enterprises example in Section 18.6 handles both flotation costs and interest subsidies.
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with equity. The net present value of the project under leverage, which we call the adjusted
present value, or the APV, is:
APV 5 NPV 1 tC 3 B
$29,918 5 2$13,000 1 .34 3 $126,229.50
That is, the value of the project when financed with some leverage is equal to the value of
the project when financed with all equity plus the tax shield from the debt. Because this
number is positive, the project should be accepted.2
You may be wondering why we chose such a precise amount of debt. Actually, we chose
it so that the ratio of debt to the present value of the project under leverage is .25.3
In this example, debt is a fixed proportion of the present value of the project, not a
fixed proportion of the initial investment of $475,000. This is consistent with the goal of
a target debt-to-market-value ratio, which we find in the real world. For example, commercial banks typically lend to real estate developers a fixed percentage of the appraised
market value of a project, not a fixed percentage of the initial investment.
18.2 Flow to Equity Approach
The flow to equity (FTE) approach is an alternative valuation approach. The formula simply calls for discounting the cash flow from the project to the equityholders of the levered
firm at the cost of equity capital, RS . For a perpetuity this becomes:
Cash
flow from project to equityholders of the levered firm
___________________________________________________
RS
There are three steps to the FTE approach.
STEP 1: CALCULATING LEVERED CASH FLOW (LCF)4
Assuming an interest rate of 10 percent, the perpetual cash flow to equityholders in our
P. B. Singer Co. example is:
Cash inflows
Cash costs
Interest (10% × $126,229.50)
Income after interest
$500,000.00
−360,000.00
−12,622.95
Corporate tax (34% tax rate)
127,377.05
−43,308.20
Levered cash flow (LCF)
$ 84,068.85
2
This example is meant to dramatize the potential importance of the tax benefits of debt. In practice, the firm will likely find the
value of a project to an all-equity firm to have at least an NPV of zero.
3
That is, the present value of the project after the initial investment has been made is $504,918 (5 $29,918 1 $475,000). Thus,
the debt-to-value ratio of the project is .25 (5 $126,229.50/$504,918).
This level of debt can be calculated directly. Note that:
Present value of levered project 5 Present value of unlevered project 1 tC 3 B
1 .34 3 .25 3 VWith debt
VWith debt 5 $462,000
Rearranging the last line, we have:
VWith debt 3 (1 2 .34 3 .25) 5 $462,000
VWith debt 5 $504,918
Debt is .25 of value: $126,229.50 5 .25 3 $504,918.
We use the term levered cash flow (LCF) for simplicity. A more complete term would be distributable cash flow (a.k.a. free cash
flow) from the project to the equityholders of a levered firm. Similarly, a more complete term for unlevered cash flow (UCF) would
be distributable cash flow (a.k.a. free cash flow) from the project to the equityholders of an unlevered firm.
4
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Alternatively, we can calculate levered cash flow (LCF) directly from unlevered cash
flow (UCF). The key here is that the difference between the cash flow that equityholders
receive in an unlevered firm and the cash flow that equityholders receive in a levered firm
is the aftertax interest payment. (Repayment of principal does not appear in this example
because the debt is perpetual.) We write this algebraically as:
UCF 2 LCF 5 (1 2 tC )RB B
The term on the right side of this expression is the aftertax interest payment. Thus, because
cash flow to the unlevered equityholders (UCF) is $92,400 and the aftertax interest payment is $8,331.15 (5.66 3 .10 3 $126,229.50), cash flow to the levered equityholders
(LCF) is:
$92,400 2 $8,331.15 5 $84,068.85
which is exactly the number we calculated earlier.
STEP 2: CALCULATING RS
The next step is to calculate the discount rate, RS . Note that we assumed that the discount rate on unlevered equity, R0, is .20. As we saw in an earlier chapter, the formula
for RS is:
B (1 − t )(R − R )
RS = R0 + __
C
0
B
S
Note that our target debt-to-value ratio of 1/4 implies a target debt-to-equity ratio of 1/3.
Applying the preceding formula to this example, we have:
1 (.66)(.20 − .10)
RS = .222 = .20 + __
3
STEP 3: VALUATION
The present value of the project’s LCF is:
$84,068.85
LCF = __________
_____
= $378,688.50
RS
.222
Because the initial investment is $475,000 and $126,229.50 is borrowed, the firm must
advance the project $348,770.50 (5$475,000 2 $126,229.50) out of its own cash reserves.
The net present value of the project is simply the difference between the present value of
the project’s LCF and the investment not borrowed. Thus, the NPV is:
$378,688.50 2 $348,770.50 5 $29,918
which is identical to the result found with the APV approach.
18.3 Weighted Average Cost
of Capital Method
Finally, we can value a project or a firm using the weighted average cost of capital
(WACC) method. Although this method was discussed in earlier chapters, it is worthwhile
to review it here. The WACC approach begins with the insight that projects of levered firms
are simultaneously financed with both debt and equity. The cost of capital is a weighted
average of the cost of debt and the cost of equity. The cost of equity is RS . Ignoring taxes,
the cost of debt is simply the borrowing rate, RB . However, with corporate taxes, the appropriate cost of debt is (1 2 tC )RB , the aftertax cost of debt.
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The formula for determining the weighted average cost of capital, RWACC, is:
S R + ______
B R (1 − t )
RWACC = ______
C
S+B S S+B B
The weight for equity, S/(S 1 B), and the weight for debt, B/(S 1 B), are target ratios.
Target ratios are generally expressed in terms of market values, not accounting values.
(Recall that another phrase for accounting value is book value.)
The formula calls for discounting the unlevered cash flow of the project (UCF) at the
weighted average cost of capital, RWACC. The net present value of the project can be written
algebraically as:
∞
UCFt
− Initial investment
∑ ___________
(1 + R
)
t=1
t
WACC
If the project is a perpetuity, the net present value is:
UCF − Initial investment
______
RWACC
We previously stated that the target debt-to-value ratio of our project is 1/4 and the
corporate tax rate is .34, implying that the weighted average cost of capital is:
3 × .222 + __
1 × .10 × .66 = .183
RWACC = __
4
4
Note that RWACC, .183, is lower than the cost of equity capital for an all-equity firm, .20.
This must always be the case because debt financing provides a tax subsidy that lowers
the average cost of capital.
We previously determined the UCF of the project to be $92,400, implying that the
present value of the project is:
$92,400
_______
= $504,918
.183
The initial investment is $475,000, so the NPV of the project is:
$504,918 2 $475,000 5 $29,918
Note that all three approaches yield the same value.
18.4 A Comparison of the APV, FTE,
and WACC Approaches
In this chapter, we provide three approaches to valuation for projects of a levered firm. The
adjusted present value (APV) approach first values the project on an all-equity basis. That
is, the project’s aftertax cash flows under all-equity financing (called unlevered cash flows,
or UCF) are placed in the numerator of the capital budgeting equation. The discount rate,
assuming all-equity financing, appears in the denominator. At this point, the calculation is
identical to that performed in the early chapters of this book. We then add the net present
value of the debt. We point out that the net present value of the debt is likely to be the sum
of four parameters: Tax effects, flotation costs, bankruptcy costs, and interest subsidies.
The flow to equity (FTE) approach discounts the aftertax cash flow from a project
going to the equityholders of a levered firm (LCF). LCF, which stands for levered cash
flow, is the residual to equityholders after interest has been deducted. The discount rate
is RS , the cost of capital to the equityholders of a levered firm. For a firm with leverage,
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RS must be greater than R0, the cost of capital for an unlevered firm. This follows from our
material in Chapter 16 showing that leverage raises the risk to the equityholders.
The last approach is the weighted average cost of capital (WACC) method. This
technique calculates the project’s aftertax cash flows assuming all-equity financing
(UCF). The UCF is placed in the numerator of the capital budgeting equation. The
denominator, R WACC, is a weighted average of the cost of equity capital and the cost of
debt capital. The tax advantage of debt is reflected in the denominator because the cost
of debt capital is determined net of corporate tax. The numerator does not reflect debt
at all.
All three approaches perform the same task: Valuation in the presence of debt
financing. And as illustrated by the previous example, all three provide the same valuation estimate. However, as we saw before, the approaches are markedly different in
technique. Because of this, students often ask questions of the following sort: “How can
this be? How can the three approaches look so different and yet give the same answer?”
We believe that the best way to handle questions like these is through the following
two points:
1. APV versus WACC: Of the three approaches, APV and WACC display the greatest similarity. After all, both approaches put the unlevered cash flow (UCF) in
the numerator. However, the APV approach discounts these flows at R0, yielding the
value of the unlevered project. Adding the present value of the tax shield gives the
value of the project under leverage. The WACC approach discounts UCF at R WACC,
which is lower than R0.
Thus, both approaches adjust the basic NPV formula for unlevered firms to
reflect the tax benefit of leverage. The APV approach makes this adjustment
directly. It simply adds in the present value of the tax shield as a separate term.
The WACC approach makes the adjustment in a more subtle way. Here, the discount
rate is lowered below R0. Although we do not provide a proof in this book, it can be
shown that these two adjustments always have the same quantitative effect.
2. Entity being valued: The FTE approach appears at first glance to be far different
from the other two. For both the APV and the WACC approaches, the initial investment is subtracted out in the final step ($475,000 in our example). However, for the
FTE approach, only the firm’s contribution to the initial investment ($348,770.50 5
$475,000 2 $126,229.50) is subtracted out. This occurs because under the FTE
approach only the future cash flows to the levered equityholders (LCF) are valued.
By contrast, future cash flows to the unlevered equityholders (UCF) are valued in
both the APV and WACC approaches. Thus, because LCFs are net of interest payments, whereas UCFs are not, the initial investment under the FTE approach is correspondingly reduced by debt financing. In this way, the FTE approach produces the
same answer that the other two approaches do.
A SUGGESTED GUIDELINE
The net present value of our project is exactly the same under each of the three methods.
In theory, this should always be the case.5 However, one method usually provides an easier
computation than another, and, in many cases, one or more of the methods are virtually
impossible computationally. We first consider when it is best to use the WACC and FTE
approaches.
5
See Ishik Inselbag and H. Kaufold, “Two DCF Approaches for Valuing Companies under Alternative Financial Strategies
(and How to Choose between Them),” Journal of Applied Corporate Finance (Spring 1997).
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If the risk of a project stays constant throughout its life, it is plausible to assume that
R0 remains constant throughout the project’s life. This assumption of constant risk appears
to be reasonable for most real-world projects. In addition, if the debt-to-value ratio remains
constant over the life of the project, both RS and RWACC will remain constant as well. Under
this latter assumption, either the FTE or the WACC approach is easy to apply. However, if
the debt-to-value ratio varies from year to year, both RS and RWACC vary from year to year
as well. Using the FTE or the WACC approach when the denominator changes every year
is computationally quite complex, and when computations become complex, the error rate
rises. Thus, both the FTE and WACC approaches present difficulties when the debt-to-value
ratio changes over time.
The APV approach is based on the level of debt in each future period. Consequently,
when the debt level can be specified precisely for future periods, the APV approach is quite
easy to use. However, when the debt level is uncertain, the APV approach becomes more
problematic. For example, when the debt-to-value ratio is constant, the debt level varies
with the value of the project. Because the value of the project in a future year cannot be
easily forecast, the level of debt cannot be easily forecast either.
Thus, we suggest the following guideline:
Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over
its life. Use APV if the project’s level of debt is known over the life of the project.
There are a number of situations where the APV approach is preferred. For example,
in a leveraged buyout (LBO) the firm begins with a large amount of debt but rapidly pays
down the debt over a number of years. Because the schedule of debt reduction in the
future is known when the LBO is arranged, tax shields in every future year can be easily
forecast. Thus, the APV approach is easy to use here. (An illustration of the APV approach
applied to LBOs is provided in the appendix to this chapter.) By contrast, the WACC and
FTE approaches are virtually impossible to apply here because the debt-to-equity value
cannot be expected to be constant over time. In addition, situations involving interest subsidies and flotation costs are much easier to handle with the APV approach. (The Bicksler
Enterprises example in Section 18.6 applies the APV approach to subsidies and flotation
costs.) Finally, the APV approach handles the lease-versus-buy decision much more easily
than does either the FTE or the WACC approach. (A full treatment of the lease-versus-buy
decision appears in a later chapter.)
The preceding examples are special cases. Typical capital budgeting situations are
more amenable to either the WACC or the FTE approach than to the APV approach.
Financial managers generally think in terms of target debt-to-value ratios. If a project does
better than expected, both its value and its debt capacity will likely rise. The manager will
increase debt correspondingly here. Conversely, the manager would be likely to reduce
debt if the value of the project were to decline unexpectedly. Of course, because financing is a time-consuming task, the ratio cannot be adjusted daily or monthly. Rather, the
adjustment can be expected to occur over the long run. As mentioned before, the WACC
and FTE approaches are more appropriate than is the APV approach when a firm focuses
on a target debt-to-value ratio.
Because of this, we recommend that the WACC and the FTE approaches, rather than
the APV approach, be used in most real-world situations. In addition, frequent discussions
with business executives have convinced us that the WACC is by far the most widely
used method in the real world. Thus, practitioners seem to agree with us that, outside of
the special situations mentioned, the APV approach is a less important method of capital
budgeting.
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The Three Methods of Valuation with Leverage
1. Adjusted present value (APV) method:
∞
UCFt
+ Additional effects of debt − Initial investment
∑ ________
(1 + R )
t
t=1
0
UCFt 5 The project’s cash flow at date t to the equityholders of an unlevered firm.
R0 5 Cost of capital for project in an unlevered firm.
2. Flow to equity (FTE) method:
∞
LCFt
− (Initial investment − Amount borrowed)
∑ ________
(1 + R )
t=1
t
S
LCFt 5 The project’s cash flow at date t to the equityholders of a levered firm.
RS 5 Cost of equity capital with leverage.
3. Weighted average cost of capital (WACC) method:
∞
UCFt
− Initial investment
∑ ___________
(1 + R
)
t=1
t
WACC
RWACC 5 Weighted average cost of capital.
Notes
1. The middle term in the APV formula implies that the value of a project with leverage
is greater than the value of the project without leverage. Because R WACC , R0, the
WACC formula implies that the value of a project with leverage is greater than the
value of the project without leverage.
2. In the FTE method, cash flow after interest (LCF) is used. Initial investment is
reduced by amount borrowed as well.
Guidelines
1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over
its life.
2. Use APV if the project’s level of debt is known over the life of the project.
18.5 Valuation When the Discount Rate
Must Be Estimated
The previous sections of this chapter introduced APV, FTE, and WACC—the three basic
approaches to valuation of a firm with leverage. However, one important detail remains.
The example in Sections 18.1 through 18.3 assumed a discount rate. We now want to show
how this rate is determined for firms with leverage, with an application to the three preceding approaches. The example in this section adds to the work in Chapters 9–13 on the
discount rate for levered and unlevered firms along with that in Chapter 16 on the effect
of leverage on the cost of capital.
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EXAMPLE
18.1
Cost of Capital World-Wide Enterprises (WWE) is a large conglomerate thinking of entering
the widget business, where it plans to finance projects with a debt-to-value ratio of 25 percent (or
a debt-to-equity ratio of 1/3). There is currently one firm in the widget industry, American Widgets
(AW). This firm is financed with 40 percent debt and 60 percent equity. The beta of AW’s equity is
1.5. AW, has a borrowing rate of 12 percent, and WWE expects to borrow for its widget venture
at 10 percent. The corporate tax rate for both firms is .40, the market risk premium is 8.5 percent,
and the riskless interest rate is 8 percent. What is the appropriate discount rate for WWE to use
for its widget venture?
As shown in Sections 18.1–18.3, a corporation may use one of three capital budgeting approaches:
APV, FTE, or WACC. The appropriate discount rates for these three approaches are R0, RS, and R WACC,
respectively. Because AW is WWE’s only competitor in widgets, we look at AW’s cost of capital to
calculate R0, RS, and R WACC for WWE’s widget venture. The following four-step procedure will allow
us to calculate all three discount rates:
1. Determining AW’s cost of equity capital: First, we determine AW’s cost of equity capital using
the security market line (SML):
AW’s Cost of Equity Capital:
__
RS 5 RF 1 b 3(RM 2 RF)
20.75% 5 8% 1 1.5 3 8.5%
__
where RM is the expected return on the market portfolio and RF is the risk-free rate.
2. Determining AW’s hypothetical all-equity cost of capital: We must standardize the preceding
number in some way because AW’s and WWE’s widget ventures have different target debt-tovalue ratios. The easiest approach is to calculate the hypothetical cost of equity capital for AW,
assuming all-equity financing. This can be determined from MM’s Proposition II under taxes:
AW’s Cost of Capital if All Equity:
B
RS = R0 + __(1 − tC )(R0 − RB )
S
.4
20.75% = R0 + __(.60)(R0 − 12%)
.6
By solving the equation, we find that R0 5 .1825. Of course, R0 is less than RS because the cost
of equity capital would be less when the firm employs no leverage.
At this point, firms in the real world generally make the assumption that the business risk of their
venture is about equal to the business risk of the firms already in the business. Applying this assumption to our problem, we assert that the hypothetical discount rate of WWE’s widget venture if all
equity financed is also .1825.6 This discount rate would be employed if WWE uses the APV approach
because the APV approach calls for R0, the project’s cost of capital in a firm with no leverage.
3. Determining RS for WWE’s widget venture: Alternatively, WWE might use the FTE approach,
where the discount rate for levered equity is determined like this:
Cost of Equity Capital for WWE’s Widget Venture:
B
RS = R0 + __(1 − tC )(R0 − RB )
S
1
19.9% = 18.25% + __(.60)(18.25% − 10%)
3
(continued)
6
Alternatively, a firm might assume that its venture would be somewhat riskier because it is a new entrant. Thus, the firm
might select a discount rate slightly higher than .1825. Of course, no exact formula exists for adjusting the discount rate
upward.
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Note that the cost of equity capital for WWE’s widget venture, .199, is less than the cost of
equity capital for AW, .2075. This occurs because AW has a higher debt-to-equity ratio. (As
mentioned, both firms are assumed to have the same business risk.)
4. Determining R WACC for WWE’s widget venture: Finally, WWE might use the WACC approach.
Here is the appropriate calculation:
RWACC for WWE’s Widget Venture:
S
B
R WACC = _____ RB(1 − tC ) + _____ RS
S+B
S+B
3
1
16.425% = __10%(.60) + __19.9%
4
4
The preceding example shows how the three discount rates, R0, RS, and RWACC, are
determined in the real world. These are the appropriate rates for the APV, FTE, and
WACC approaches, respectively. Note that RS for American Widgets is determined first
because the cost of equity capital can be determined from the beta of the firm’s stock.
As discussed in an earlier chapter, beta can easily be estimated for any publicly traded
firm such as AW.
18.6 APV Example
As mentioned earlier in this chapter, firms generally set a target debt-to-equity ratio, allowing the use of WACC and FTE for capital budgeting. APV does not work as well here.
However, as we also mentioned earlier, APV is the preferred approach when there are side
benefits and side costs to debt. Because the analysis here can be tricky, we now devote an
entire section to an example where, in addition to the tax subsidy to debt, both flotation
costs and interest subsidies come into play.
EXAMPLE
18.2
APV Bicksler Enterprises is considering a $10 million project that will last five years, implying
straight-line depreciation per year of $2 million. The cash revenues less cash expenses per year are
$3,500,000. The corporate tax bracket is 34 percent. The risk-free rate is assumed to be 10 percent,
and the cost of unlevered equity is 20 percent.
The cash flow projections each year are these:
CF0
Initial outlay
Depreciation
tax shield
Revenue less
expenses
CF1
CF2
CF3
CF4
CF5
.34 × $2,000,000
= $680,000
(1 − .34) × $3,500,000
= $2,310,000
$ 680,000
$ 680,000
$ 680,000
$ 680,000
$2,310,000
$2,310,000
$2,310,000
$2,310,000
−$10,000,000
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We stated before that the APV of a project is the sum of its all-equity value plus the additional effects
of debt. We examine each in turn.
All-Equity Value
Assuming the project is financed with all equity, the value of the project is:
$680,000
$2,310,000
1 5
1 5
−$10,000,000 + _______ × 1 − ____ + _________ × 1 − ____ = −$513,951
.10
1.10
.20
1.20
[ ( )]
[ ( )]
Initial cost + Depreciation tax shield + Present value of (Cash revenues − Cash expenses)
This calculation uses the techniques presented in the early chapters of this book. Notice that the
depreciation tax shield is discounted at the riskless rate of 10 percent (or sometimes at a rate a little
higher). The revenues and expenses are discounted at the higher rate of 20 percent.
An all-equity firm would clearly reject this project because the NPV is −$513,951. And equity
flotation costs (not mentioned yet) would only make the NPV more negative. However, debt financing may add enough value to the project to justify acceptance. We consider the effects of debt next.
Additional Effects of Debt Bicksler Enterprises can obtain a five-year, nonamortizing loan for
$7,500,000 after flotation costs at the risk-free rate of 10 percent. Flotation costs are fees paid when
stock or debt is issued. These fees may go to printers, lawyers, and investment bankers, among others. Bicksler Enterprises is informed that flotation costs will be 1 percent of the gross proceeds of its
loan. The previous chapter indicates that debt financing alters the NPV of a typical project. We look
at the effects of debt next.
Flotation Costs
Given that flotation costs are 1 percent of the gross proceeds, we have:
$7,500,000 = (1 − .01) × Gross proceeds = .99 × Gross proceeds
Thus, the gross proceeds are:
$7,500,000
__________
1 − .01
$7,500,000
= __________ = $7,575,758
.99
This implies flotation costs of $75,758 (51% 3 $7,575,758). To check the calculation, note that net
proceeds are $7,500,000 (5$7,575,758 2 $75,758). In other words, Bicksler Enterprises receives
only $7,500,000. The flotation costs of $75,758 are received by intermediaries such as investment
bankers.
Flotation costs are paid immediately but are deducted from taxes by amortizing on a straight-line
basis over the life of the loan. The cash flows from flotation costs are as follows:
Date 0
Flotation costs
Deduction
Date 1
Date 2
Date 3
Date 4
Date 5
$75,758
_______
= $15,152
$15,152
$15,152
$15,152
$15,152
.34 × $15,152
= $ 5,152
$ 5,152
$ 5,152
$ 5,152
$ 5,152
−$75,758
5
Tax shield from
flotation costs
The relevant cash flows from flotation costs are in boldface. When we discount at 10 percent, the
tax shield has a net present value of:
$5,152 × PVIFA5.10 = $19,530
This implies a net cost of flotation of:
2$75,758 1 $19,530 5 2$56,228
(continued)
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Capital Structure and Dividend Policy
The net present value of the project after the flotation costs of debt but before the benefits of
debt is:
2$513,951 2 $56,228 5 2$570,179
Tax Subsidy Interest must be paid on the gross proceeds of the loan, even though intermediaries
receive the flotation costs. Because the gross proceeds of the loan are $7,575,758, annual interest
is $757,576 (5 $7,575,758 3 .10). The interest cost after taxes is $500,000 [5 $757,576 3 (1 2
.34)]. Because the loan is nonamortizing, the entire debt of $7,575,758 is repaid at Date 5. These
terms are indicated here:
Date 0
Loan (gross proceeds)
Interest paid
Interest cost
after taxes
Repayment of debt
Date 1
Date 2
Date 3
Date 4
Date 5
$ 757,576
$ 757,576
$ 757,576
$
$500,000
$500,000
$500,000
$ 500,000
$7,575,758
$7,575,758
10% × $7,575,758
= $757,576
(1 − .34) × $757,576
= $500,000
757,576
The relevant cash flows are listed in boldface in the preceding table. They are (1) loan received,
(2) annual interest cost after taxes, and (3) repayment of debt. Note that we include the gross proceeds of the loan as an inflow because the flotation costs have previously been subtracted.
In Chapter 16 we mentioned that the financing decision can be evaluated in terms of net present
value. The net present value of the loan is simply the sum of the net present values of each of the
three cash flows. This can be represented as follows:
Present value
of loan
repayments
(18.1)
$7,575,758
[ ( ) ] − __________
(1.10)
(18.1′)
APV = All-equity value − Flotation costs of debt + NPV (loan)
(18.2)
NPV (loan) = +
Amount
borrowed
−
Present value
of aftertax
interest payments
−
The calculations for this example are:
$500,000
1
$976,415 = +$7,575,758 − ________ × 1 − ____
.10
1.10
The NPV (loan) is positive, reflecting the interest tax shield.7
The adjusted present value of the project with this financing is:
$406,236 =
−$513,951 −
5
5
+ $976,415
$56,228
(18.2′)
Though we previously saw that an all-equity firm would reject the project, a firm would accept the
project if a $7,500,000 (net) loan could be obtained.
Because the loan just discussed was at the market rate of 10 percent, we have considered only
two of the three additional effects of debt (flotation costs and tax subsidy) so far. We now examine
another loan where the third effect arises.
7
The NPV (loan) must be zero in a no-tax world because interest provides no tax shield there. To check this intuition,
we calculate:
$7,575,758
[ ( ) ] − __________
(1.10)
$757,576
1
No-tax case: 0 = +$7,575,758 − ________ × 1 − ____
.10
1.10
5
5
CHAPTER 18 Valuation and Capital Budgeting for the Levered Firm
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567
Non–Market-Rate Financing A number of companies are fortunate enough to obtain subsidized
financing from a governmental authority. Suppose that the project of Bicksler Enterprises is deemed
socially beneficial and the state of New Jersey grants the firm a $7,500,000 loan at 8 percent interest.
In addition, all flotation costs are absorbed by the state. Clearly, the company will choose this loan
over the one we previously calculated. Here are the cash flows from the loan:
Date 0
Loan received
Interest paid
Aftertax interest
Date 1
Date 2
Date 3
Date 4
Date 5
$ 600,000
$ 600,000
$ 600,000
$
$396,000
$396,000
$396,000
$ 396,000
$7,500,000
$7,500,000
8% × $7,500,000
= $600,000
(1 − .34) × $600,000
= $396,000
Repayment of debt
600,000
The relevant cash flows are listed in boldface in the preceding table. Using Equation 18.1, the
NPV (loan) is:
$396,000
1
$1,341,939 = +$7,500,000 − ________ × 1 − ____
.10
1.10
$7,500,000
[ ( ) ] − __________
(1.10)
5
5
(18.1″)
Why do we discount the cash flows in Equation 18.1˝ at 10 percent when the firm is borrowing at 8 percent? We discount at 10 percent because that is the fair or marketwide rate. That is,
10 percent is the rate at which the firm could borrow without benefit of subsidization. The net present
value of the subsidized loan is larger than the net present value of the earlier loan because the firm
is now borrowing at the below-market rate of 8 percent. Note that the NPV (loan) calculation in
Equation 18.1˝ captures both the tax effect and the non–market-rate effect.
The net present value of the project with subsidized debt financing is:
APV = All-equity value − Flotation costs of debt + NPV (loan)
(18.2)
+ $1,341,939
(18.2″)
+$827,988 = −$513,951
−
0
The preceding example illustrates the adjusted present value (APV) approach. The
approach begins with the present value of a project for the all-equity firm. Next, the effects
of debt are added in. The approach has much to recommend it. It is intuitively appealing
because individual components are calculated separately and added together in a simple
way. And, if the debt from the project can be specified precisely, the present value of the
debt can be calculated precisely.
18.7 Beta and Leverage
A previous chapter provides the formula for the relationship between the beta of the common stock and leverage of the firm in a world without taxes. We reproduce this formula
here:
The No-Tax Case:
(
Debt
βEquity = βAsset 1 + ______
Equity
)
(18.3)
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PART IV
Capital Structure and Dividend Policy
As pointed out earlier, this relationship holds under the assumption that the beta of debt
is zero.
Because firms must pay corporate taxes in practice, it is worthwhile to provide the
relationship in a world with corporate taxes. It can be shown that the relationship between
the beta of the unlevered firm and the beta of the levered equity is this:8
The Corporate Tax Case:
(1 − tC)Debt
βEquity = 1 + ___________
βUnlevered firm
Equity
(
)
(18.4)
when (1) the corporation is taxed at the rate of tC and (2) the debt has a zero beta.
Because [1 1 (1 2 tC) Debt/Equity] must be more than 1 for a levered firm, it follows
that bUnlevered firm < bEquity. The corporate tax case of Equation 18.4 is quite similar to the notax case of Equation 18.3 because the beta of levered equity must be greater than the beta
of the unlevered firm in either case. The intuition that leverage increases the risk of equity
applies in both cases.
However, notice that the two equations are not equal. It can be shown that leverage
increases the equity beta less rapidly under corporate taxes. This occurs because, under
taxes, leverage creates a riskless tax shield, thereby lowering the risk of the entire firm.
8
This result holds only if the beta of debt equals zero. To see this, note that:
VU + tCB = VL = B + S
(a)
where:
VU 5 Value of unlevered firm.
VL 5 Value of levered firm.
B 5 Value of debt in a levered firm.
S 5 Value of equity in a levered firm.
As we stated in the text, the beta of the levered firm is a weighted average of the debt beta and the equity beta:
S ×β
B × β + ______
______
B
S
B+S
B+S
where bB and bS are the betas of the debt and the equity of the levered firm, respectively. Because VL 5 B 1 S, we have:
S ×β
B × β + ___
___
B
S
VL
VL
(b)
The beta of the levered firm can also be expressed as a weighted average of the beta of the unlevered firm and the beta of
the tax shield:
V
VU + tCB
tB
VU + tCB
U
C
_________
× βU + _________
× βB
where bU is the beta of the unlevered firm. This follows from Equation (a). Because VL 5 VU 1 tCB, we have:
V
VL
tB
VL
U
C
___
× βU + ____
× βB
(c)
We can equate (b) and (c) because both represent the beta of a levered firm. Equation (a) tells us that VU 5 S 1 (1 2 tC) 3 B.
Under the assumption that bB 5 0, equating (b) and (c) and using Equation (a) yields Equation 18.4.
The generalized formula for the levered beta (where bB is not zero) is:
B
βS = βU + (1 − tC) (βU − βB ) __
S
and:
B(1 − tC)
S
βU = ____________
β + ____________
β
B(1 − tC) + S S B(1 − tC) + S B
CHAPTER 18 Valuation and Capital Budgeting for the Levered Firm
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569
EXAMPLE
18.3
Unlevered Betas C. F. Lee, Incorporated, is considering a scale-enhancing project. The market
value of the firm’s debt is $100 million, and the market value of the firm’s equity is $200 million. The
debt is considered riskless. The corporate tax rate is 34 percent. Regression analysis indicates that
the beta of the firm’s equity is 2. The risk-free rate is 10 percent, and the expected market premium
is 8.5 percent. What would the project’s discount rate be in the hypothetical case that C. F. Lee, Inc.,
is all equity?
We can answer this question in two steps.
1. Determining beta of hypothetical all-equity firm: Rearranging Equation 18.4, we have this:
Unlevered Beta:
Equity
______________________
Equity + (1 − tC) × Debt
× βEquity = βUnlevered firm
$200 million
__________________________________
$200 million + (1 − .34) × $100 million
(18.5)
× 2 = 1.50
2. Determining discount rate: We calculate the discount rate from the security market line (SML)
as follows:
Discount Rate:
__
RS = RF + β × [RM − RF]
22.75% = 10% + 1.50 × 8.5%
THE PROJECT IS NOT SCALE ENHANCING
Because the previous example assumed that the project is scale enhancing, we began with
the beta of the firm’s equity. If the project is not scale enhancing, we could begin with the
equity betas of firms in the industry of the project. For each firm, we could calculate the
hypothetical beta of the unlevered equity by Equation 18.5. The SML could then be used
to determine the project’s discount rate from the average of these betas.
EXAMPLE
18.4
More Unlevered Betas The J. Lowes Corporation, which currently manufactures staples, is
considering a $1 million investment in a project in the aircraft adhesives industry. The corporation
estimates unlevered aftertax cash flows (UCF) of $300,000 per year into perpetuity from the project.
The firm will finance the project with a debt-to-value ratio of .5 (or, equivalently, a debt-to-equity
ratio of 1.0).
The three competitors in this new industry are currently unlevered, with betas of 1.2, 1.3, and
1.4. Assuming a risk-free rate of 5 percent, a market risk premium of 9 percent, and a corporate tax
rate of 34 percent, what is the net present value of the project?
We can answer this question in five steps.
1. Calculating the average unlevered beta in the industry: The average unlevered beta across all three
existing competitors in the aircraft adhesives industry is:
1.2
+ 1.3 + 1.4
______________
= 1.3
3
(continued)
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PART IV
Capital Structure and Dividend Policy
2. Calculating the levered beta for J. Lowes’s new project : Assuming the same unlevered beta for this
new project as for the existing competitors, we have, from Equation 18.4:
Levered Beta:
(1 − tC) Debt
βUnlevered firm
βEquity = 1 + ____________
Equity
(
)
.66 × 1
2.16 = 1 + _______
× 1.3
1
3. Calculating the cost of levered equity for the new project: We calculate the discount rate from the
security market line (SML) as follows:
(
)
Discount Rate:
__
RS = RF + β × [RM − RF]
.244 = .05 + 2.16 × .09
4. Calculating the WACC for the new project: The formula for determining the weighted average cost
of capital, RWACC, is:
S
B
__
RWACC = __
V RB(1 − tC) + V RS
1
1
.139 = __ × .05 × .66 + __ × .244
2
2
5. Determining the project’s value: Because the cash flows are perpetual, the NPV of the project is:
Unlevered
cash flows (UCF)
_______________________
− Initial investment
RWACC
$300,000
________
.139
− $1 million = $1.16 million
Summary and Conclusions
Earlier chapters of this text showed how to value projects and entire firms with and without
leverage. In the last three chapters we discuss how to determine the optimal amount of leverage. We pointed out that the introduction of taxes and bankruptcy costs changes a firm’s
financing decisions. Most rational corporations should employ some debt in a world of this
type. The present chapter has discussed three methods for valuation by levered firms: the
adjusted present value (APV), flow to equity (FTE), and weighted average cost of capital
(WACC) approaches.
Concept Questions
1.
APV
2.
WACC and APV What is the main difference between the WACC and APV methods?
3.
FTE What is the main difference between the FTE approach and the other two
approaches?
How is the APV of a project calculated?
CHAPTER 18 Valuation and Capital Budgeting for the Levered Firm
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571
4.
Capital Budgeting You are determining whether your company should undertake a
new project and have calculated the NPV of the project using the WACC method when
the CFO, a former accountant, notices that you did not use the interest payments in
calculating the cash flows of the project. What should you tell him? If he insists that you
include the interest payments in calculating the cash flows, what method can you use?
5.
Beta and Leverage What are the two types of risk that are measured by a levered beta?
Questions and Problems
1.
NPV and APV Zoso is a rental car company that is trying to determine whether to add
25 cars to its fleet. The company fully depreciates all its rental cars over five years using
the straight-line method. The new cars are expected to generate $215,000 per year in
earnings before taxes and depreciation for five years. The company is entirely financed
by equity and has a 35 percent tax rate. The required return on the company’s unlevered
equity is 13 percent, and the new fleet will not change the risk of the company.
a. What is the maximum price that the company should be willing to pay for the new
fleet of cars if it remains an all-equity company?
b. Suppose the company can purchase the fleet of cars for $650,000. Additionally,
assume the company can issue $430,000 of five-year debt to finance the project at the
risk-free rate of 8 percent. All principal will be repaid in one balloon payment at the
end of the fifth year. What is the adjusted present value (APV) of the project?
2.
APV Gemini, Inc., an all-equity firm, is considering an investment of $1.4 million
that will be depreciated according to the straight-line method over its four-year life.
The project is expected to generate earnings before taxes and depreciation of $502,000
per year for four years. The investment will not change the risk level of the firm. The
company can obtain a four-year, 9.5 percent loan to finance the project from a local
bank. All principal will be repaid in one balloon payment at the end of the fourth
year. The bank will charge the firm $45,000 in flotation fees, which will be amortized
over the four-year life of the loan. If the company financed the project entirely
with equity, the firm’s cost of capital would be 13 percent. The corporate tax rate is
30 percent. Using the adjusted present value method, determine whether the company
should undertake the project.
3.
FTE Milano Pizza Club owns three identical restaurants popular for their specialty
pizzas. Each restaurant has a debt–equity ratio of 40 percent and makes interest payments
of $41,000 at the end of each year. The cost of the firm’s levered equity is 19 percent.
Each store estimates that annual sales will be $1.45 million; annual cost of goods sold
will be $785,000; and annual general and administrative costs will be $435,000. These
cash flows are expected to remain the same forever. The corporate tax rate is 40 percent.
a. Use the flow to equity approach to determine the value of the company’s equity.
b. What is the total value of the company?
4.
WACC If Wild Widgets, Inc., were an all-equity company, it would have a beta of .95.
The company has a target debt–equity ratio of .40. The expected return on the market
portfolio is 11 percent, and Treasury bills currently yield 4 percent. The company has one
bond issue outstanding that matures in 20 years and has a coupon rate of 6.5 percent. The
bond currently sells for $1,080. The corporate tax rate is 34 percent.
a. What is the company’s cost of debt?
b. What is the company’s cost of equity?
c. What is the company’s weighted average cost of capital?
BASIC
(Questions 1–9)
572
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PART IV
5.
Capital Structure and Dividend Policy
Beta and Leverage North Pole Fishing Equipment Corporation and South Pole Fishing
Equipment Corporation would have identical equity betas of 1.10 if both were all equity
financed. The market value information for each company is shown here:
Debt
Equity
North Pole
South Pole
$2,700,000
$3,900,000
$3,900,000
$2,700,000
The expected return on the market portfolio is 10.9 percent, and the risk-free rate is
3.2 percent. Both companies are subject to a corporate tax rate of 35 percent. Assume
the beta of debt is zero.
a. What is the equity beta of each of the two companies?
b. What is the required rate of return on each of the two companies’ equity?
6.
NPV of Loans Daniel Kaffe, CFO of Kendrick Enterprises, is evaluating a 10-year,
7.5 percent loan with gross proceeds of $4,450,000. The interest payments on the loan
will be made annually. Flotation costs are estimated to be 2.5 percent of gross proceeds
and will be amortized using a straight-line schedule over the 10-year life of the loan. The
company has a tax rate of 40 percent, and the loan will not increase the risk of financial
distress for the company.
a. Calculate the net present value of the loan excluding flotation costs.
b. Calculate the net present value of the loan including flotation costs.
7.
NPV for an All-Equity Company Watson, Inc., is an all-equity firm. The cost of the
company’s equity is currently 11.9 percent, and the risk-free rate is 3.5 percent. The company
is currently considering a project that will cost $10.6 million and last six years. The project
will generate revenues minus expenses each year in the amount of $3.1 million. If the
company has a tax rate of 40 percent, should it accept the project?
8.
WACC National Electric Company (NEC) is considering a $68 million project in its
power systems division. Tom Edison, the company’s chief financial officer, has evaluated
the project and determined that the project’s unlevered cash flows will be $4.4 million
per year in perpetuity. Mr. Edison has devised two possibilities for raising the initial
investment: issuing 10-year bonds or issuing common stock. The company’s pretax
cost of debt is 6.4 percent, and its cost of equity is 10.8 percent. The company’s target
debt-to-value ratio is 80 percent. The project has the same risk as the company’s existing
businesses, and it will support the same amount of debt. The tax rate is 34 percent.
Should NEC accept the project?
9.
WACC
Bolero, Inc., has compiled the following information on its financing costs:
Type of Financing
Book Value
Market Value
Cost
Short-term debt
$12,000,000
$12,500,000
Long-term debt
20,000,000
23,000,000
7.2
Common stock
9,000,000
54,000,000
13.8
$41,000,000
$89,500,000
Total
4.1%
The company is in the 35 percent tax bracket and has a target debt–equity ratio of
60 percent. The target short-term debt/long-term debt ratio is 20 percent.
a. What is the company’s weighted average cost of capital using book value weights?
b. What is the company’s weighted average cost of capital using market value weights?
CHAPTER 18 Valuation and Capital Budgeting for the Levered Firm
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573
c. What is the company’s weighted average cost of capital using target capital structure
weights?
d. What is the difference between WACCs? Which is the correct WACC to use for
project evaluation?
INTERMEDIATE
(Questions 10–14)
10.
APV Triad Corporation has established a joint venture with Tobacco Road Construction,
Inc., to build a toll road in North Carolina. The initial investment in paving equipment is
$93 million. The equipment will be fully depreciated using the straight-line method over
its economic life of five years. Earnings before interest, taxes, and depreciation collected
from the toll road are projected to be $12.9 million per annum for 20 years starting from
the end of the first year. The corporate tax rate is 35 percent. The required rate of return
for the project under all-equity financing is 13 percent. The pretax cost of debt for the
joint partnership is 8.5 percent. To encourage investment in the country’s infrastructure,
the U.S. government will subsidize the project with a $30 million, 15-year loan at an
interest rate of 5 percent per year. All principal will be repaid in one balloon payment at
the end of Year 15. What is the adjusted present value of this project?
11.
APV For the company in the previous problem, what is the value of being able to issue
subsidized debt instead of having to issue debt at the terms it would normally receive?
Assume the face amount and maturity of the debt issue are the same.
12.
APV MVP, Inc., has produced rodeo supplies for over 20 years. The company
currently has a debt–equity ratio of 50 percent and is in the 40 percent tax bracket. The
required return on the firm’s levered equity is 16 percent. The company is planning to
expand its production capacity. The equipment to be purchased is expected to generate
the following unlevered cash flows:
Year
Cash Flow
0
1
–$15,100,000
5,400,000
2
8,900,000
3
8,600,000
The company has arranged a debt issue of $8.7 million to partially finance the expansion.
Under the loan, the company would pay interest of 9 percent at the end of each year on
the outstanding balance at the beginning of the year. The company would also make yearend principal payments of $2,900,000 per year, completely retiring the issue by the end
of the third year. Using the adjusted present value method, should the company proceed
with the expansion?
13.
WACC Neon Corporation’s stock returns have a covariance with the market portfolio of
.0415. The standard deviation of the returns on the market portfolio is 20 percent, and the
expected market risk premium is 7.5 percent. The company has bonds outstanding with
a total market value of $45 million and a yield to maturity of 6.5 percent. The company
also has 4.2 million shares of common stock outstanding, each selling for $30. The
company’s CEO considers the firm’s current debt–equity ratio optimal. The corporate
tax rate is 35 percent, and Treasury bills currently yield 3.4 percent. The company is
considering the purchase of additional equipment that would cost $47 million. The
expected unlevered cash flows from the equipment are $13.5 million per year for five
years. Purchasing the equipment will not change the risk level of the firm.
a. Use the weighted average cost of capital approach to determine whether Neon should
purchase the equipment.
b. Suppose the company decides to fund the purchase of the equipment entirely with
debt. What is the cost of capital for the project now? Explain.
574
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CHALLENGE
(Questions 15–18)
PART IV
Capital Structure and Dividend Policy
14.
Beta and Leverage Dorman Industries has a new project available that requires an initial
investment of $4.3 million. The project will provide unlevered cash flows of $710,000 per
year for the next 20 years. The company will finance the project with a debt-to-value ratio
of .40. The company’s bonds have a YTM of 6.8 percent. The companies with operations
comparable to this project have unlevered betas of 1.15, 1.08, 1.30, and 1.25. The risk-free
rate is 3.8 percent, and the market risk premium is 7 percent. The company has a tax rate of
34 percent. What is the NPV of this project?
15.
APV, FTE, and WACC Newkirk, Inc., is an unlevered firm with expected annual
earnings before taxes of $21 million in perpetuity. The current required return on the firm’s
equity is 16 percent, and the firm distributes all of its earnings as dividends at the end of
each year. The company has 1.3 million shares of common stock outstanding and is subject
to a corporate tax rate of 35 percent. The firm is planning a recapitalization under which it
will issue $30 million of perpetual 9 percent debt and use the proceeds to buy back shares.
a. Calculate the value of the company before the recapitalization plan is announced.
What is the value of equity before the announcement? What is the price per share?
b. Use the APV method to calculate the company value after the recapitalization plan is
announced. What is the value of equity after the announcement? What is the price per share?
c. How many shares will be repurchased? What is the value of equity after the repurchase has been completed? What is the price per share?
d. Use the flow to equity method to calculate the value of the company’s equity after
the recapitalization.
16.
APV, FTE, and WACC Mojito Mint Company has a debt–equity ratio of .35. The required
return on the company’s unlevered equity is 12.8 percent, and the pretax cost of the firm’s
debt is 6.5 percent. Sales revenue for the company is expected to remain stable indefinitely at
last year’s level of $17,500,000. Variable costs amount to 60 percent of sales. The tax rate is
40 percent, and the company distributes all its earnings as dividends at the end of each year.
a. If the company were financed entirely by equity, how much would it be worth?
b. What is the required return on the firm’s levered equity?
c. Use the weighted average cost of capital method to calculate the value of the company.
What is the value of the company’s equity? What is the value of the company’s debt?
d. Use the flow to equity method to calculate the value of the company’s equity.
17.
APV, FTE, and WACC Bruin Industries just issued $265,000 of perpetual 8 percent
debt and used the proceeds to repurchase stock. The company expects to generate
$123,000 of earnings before interest and taxes in perpetuity. The company distributes all
its earnings as dividends at the end of each year. The firm’s unlevered cost of capital is
14 percent, and the corporate tax rate is 40 percent.
a. What is the value of the company as an unlevered firm?
b. Use the adjusted present value method to calculate the value of the company with
leverage.
c. What is the required return on the firm’s levered equity?
d. Use the flow to equity method to calculate the value of the company’s equity.
18.
Projects That Are Not Scale Enhancing Blue Angel, Inc., a private firm in the
holiday gift industry, is considering a new project. The company currently has a target
debt–equity ratio of .40, but the industry target debt–equity ratio is .35. The industry
average beta is 1.2. The market risk premium is 7 percent, and the risk-free rate is
5 percent. Assume all companies in this industry can issue debt at the risk-free
rate. The corporate tax rate is 40 percent. The project requires an initial outlay of
$785,000 and is expected to result in a $93,000 cash inflow at the end of the first
year. The project will be financed at the company’s target debt–equity ratio. Annual
cash flows from the project will grow at a constant rate of 5 percent until the end
of the fifth year and remain constant forever thereafter. Should Blue Angel invest in
the project?
CHAPTER 18 Valuation and Capital Budgeting for the Levered Firm
Mini Case
■■■
575
THE LEVERAGED BUYOUT OF CHEEK PRODUCTS, INC.
Cheek Products, Inc. (CPI) was founded 53 years ago by Joe Cheek and originally sold snack
foods such as potato chips and pretzels. Through acquisitions, the company has grown into
a conglomerate with major divisions in the snack food industry, home security systems, cosmetics, and plastics. Additionally, the company has several smaller divisions. In recent years,
the company has been underperforming, but the company’s management doesn’t seem to be
aggressively pursuing opportunities to improve operations (or the stock price).
Meg Whalen is a financial analyst specializing in identifying potential buyout targets.
She believes that two major changes are needed at Cheek. First, she thinks that the company
would be better off if it sold several divisions and concentrated on its core competencies in
snack foods and home security systems. Second, the company is financed entirely with equity.
Because the cash flows of the company are relatively steady, Meg thinks the company’s debt–
equity ratio should be at least .25. She believes these changes would significantly enhance
shareholder wealth, but she also believes that the existing board and company management are
unlikely to take the necessary actions. As a result, Meg thinks the company is a good candidate
for a leveraged buyout.
A leveraged buyout (LBO) is the acquisition by a small group of equity investors of a
public or private company. Generally, an LBO is financed primarily with debt. The new shareholders service the heavy interest and principal payments with cash from operations and/or
asset sales. Shareholders generally hope to reverse the LBO within three to seven years by way
of a public offering or sale of the company to another firm. A buyout is therefore likely to be
successful only if the firm generates enough cash to service the debt in the early years and if
the company is attractive to other buyers a few years down the road.
Meg has suggested the potential LBO to her partners, Ben Feller and Brenton Flynn. Ben
and Brenton have asked Meg to provide projections of the cash flows for the company. Meg
has provided the following estimates (in millions):
2015
2016
2017
2018
2019
$2,749
$3,083
$3,322
$3,400
$3,539
Costs
731
959
1,009
1,091
1,149
Depreciation
485
516
537
564
575
EBT
$1,533
$1,608
$1,776
$1,745
$1,815
Capital expenditures
$ 279
$ 242
$ 304
$ 308
$ 304
−$ 122
−$ 186
$ 101
$
$ 108
$1,419
$1,028
Sales
Change in NWC
Asset sales
95
At the end of five years, Meg estimates that the growth rate in cash flows will be 3.5 percent per year. The capital expenditures are for new projects and the replacement of equipment
that wears out. Additionally, the company would realize cash flow from the sale of several divisions. Even though the company will sell these divisions, overall sales should increase because
of a more concentrated effort on the remaining divisions.
After plowing through the company’s financials and various pro forma scenarios, Ben and
Brenton feel that in five years they will be able to sell the company to another party or take it
public again. They are also aware that they will have to borrow a considerable amount of the
purchase price. The interest payments on the debt for each of the next five years if the LBO is
undertaken will be these (in millions):
Interest payments
2015
2016
2017
2018
2019
$1,927
$1,859
$2,592
$2,526
$2,614
576
■■■
PART IV
Capital Structure and Dividend Policy
The company currently has a required return on assets of 14 percent. Because of the high
debt level, the debt will carry a yield to maturity of 12.5 percent for the next five years. When
the debt is refinanced in five years, they believe the new yield to maturity will be 8 percent.
CPI currently has 425 million shares of stock outstanding that sell for $29 per share. The
corporate tax rate is 40 percent. If Meg, Ben, and Brenton decide to undertake the LBO, what
is the most they should offer per share?
Appendix 18A
The Adjusted Present Value Approach
to Valuing Leveraged Buyouts
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